Are Tornadoes Getting Stronger?

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1 Are Getting Stronger? Department of Geography, Florida State University Thomas Jagger, Ian Elsner

2 Categorical Scale for Tornado Intensity The EF damage scale to rate tornado intensity is categorical. An estimate of how strong a tornado can get requires a continuous intensity scale. We can count the number of tornadoes by EF rating, including the number of violent (EF4 and EF5) tornadoes. But a time series of the number of tornadoes by EF rating does not answer the question: Are tornadoes getting stronger?

3 If We Solve This, Then Year Tornado Wind Speed (m s 1 )

4 What are tornadoes?

5 How do they form?

6 Path length & path width

7 Path length, width, & EF category Path Length (km) EF Category A Path Width (km) EF Category B Path Length (m) Path Width (m) EF C

8 Path length, width, & EF category Table: Damage path statistics. Data are based on all reported tornadoes in the United States ( ). N is the sample size. The lower and upper quartile values are given in parentheses. Length (km) Width (m) Category N Mean Median Mean Median EF (1.61,8.05) (45.7,137.2) EF (3.54,17.03) EF (9.90,35.40) EF (16.09,56.73) EF (45.51,65.93) (91.4,365.8) (228.6,804.7) (443.5,1063.0) (1207.0,1609.3) Since 1994 the U.S. has been almost completely covered by NOAA s WSR-88D radar.

9 Model for EF category Tornado category model (cumulative logistic) logit[p(t i f )] = (θ f β 1 L i 1/3 β 2 W i 1/2 β 3 L i 1/3 W i 1/2 ) exp(ζ 1 L i 1/3 + ζ 2 W i 1/2 ) for i = 1,..., n and f = 1,..., 4, where P(T i f ) is the probability of tornado i having an EF category f or lower. We use the square root of the width and cube root of the length so that the model conforms to the proportional odds assumption meaning that the relationship between the EF1 category and all higher categories is the same as the relationship between the EF2 category and all higher categories, and so on.

10 The model includes a term to correct for the population bias Tornado Reports/10 km Distance to Nearest City Center (km)

11 The bias is decreasing with time Tornado Reports/100 km 2 per Decade Distance From Nearest City Center (km)

12 Model for tornado wind speed Given the path length and width of a tornado we compute the probability across the EF scale then take the inner product of this probability vector with the vector of characteristic wind speeds for each category. 600 Frequency Predicted Tornado Intensity (m s 1 )

13 EF scale and intensity ranges Mean Estimated Intensity (m s 1 ) EF Rating

14 Predictions (out of sample) L W Est. Peak Model Peak Tornado Date (mi) (mi) Wind (m/s) Wind (m/s) Adairsville, GA 1/30/ Moore, OK 5/20/ El Reno, OK 5/31/ Wayne, NE 10/4/

Doppler on Wheels The derived radar wind speeds are independent of damage estimates and result from a calibration with nearby WSR-88D measurements. The wind speeds correlate at.82 (.46,.

15 Doppler on Wheels The derived radar wind speeds are independent of damage estimates and result from a calibration with nearby WSR-88D measurements. The wind speeds correlate at.82 (.46,.95) [95% CI, n = 12]. Although only a small sample of tornadoes, the radar-estimated wind values range from a low of 38 m s 1 to a high of 91 m s 1 suggesting the potential for our model to be applicable throughout the database.

16 Mass-specific kinetic energy Scale analysis shows cyclostrophic balance (pressure gradient force equals the centrifugal force) in tornadoes at peak intensity. Assuming a linearly increasing velocity with radius r, the solution of the integral over the centrifugal force is the mass-specific kinetic energy (E) given by E = ro 0 F (r)dr = v 2 /2, where v is the fastest wind inside the tornado.

17 Mass-specific kinetic energy trends Mass Specific Kinetic Energy (J/kg) Year

18 Integrated kinetic energy Intensity (m s 1 ) Percent Threshold Area

19 Integrated kinetic energy histogram 1500 Number of ( ) Integrated Kinetic Energy (J)

20 Integrated kinetic energy trends Integrated Kinetic Energy (GJ) Year

21 Final words These findings suggest an important new area of hazard research. How climate affects tornadoes and other severe local storms. 1st International Summit on and Climate Change: Crete Greece, May 25-30, Thank you. Questions?

Examples of extreme event modeling in tornado and hurricane research

Examples of extreme event modeling in tornado and hurricane research James B. Elsner Twitter: @JBElsner Florida State University, Tallahassee, FL June 15, 2015 Help: Thomas H. Jagger Are Tornadoes More